Abstract We give a general method for constructing examples of transcendental entire functions given small order, which allows precise control over the size and shape set where minimum modulus function is relatively large. Our involves novel technique to obtain an upper bound growth positive harmonic defined in certain type multiply connected domain, based on comparing Harnack metric hyperbolic...

by the method of weight coefficients, techniques of real analysis andhermite-hadamard's inequality, a half-discrete hardy-hilbert-type inequalityrelated to the kernel of the hyperbolic cosecant function with the best possibleconstant factor expressed in terms of the extended riemann-zeta function is proved.the more accurate equivalent forms, the operator expressions with the norm,the reverses a...

A subclass of recently discovered class of solutions in multidimensional gravity with intersecting p-branes related to Lie algebras and governed by a set of harmonic functions is considered. This subclass in case of three Euclidean p-branes (one electric and two magnetic) contains a cosmological solution to D = 11 supergravity related to hyperbolic Kac-Moody algebra F 3 (of rank 3). This soluti...

We prove that a quasiconformal map of the sphere S admits a harmonic quasi-isometric extension to the hyperbolic space H, thus confirming the well known Schoen Conjecture in dimension 3.

We prove Liouville theorems for Dirac-harmonic maps from the Euclidean space Rn, the hyperbolic space Hn and a Riemannian manifold Sn (n ≥ 3) with the Schwarzschild metric to any Riemannian manifold N .

We construct a one-to-one continuous map from the Morse boundary of hierarchically hyperbolic group to its Martin boundary. This construction is based on deviation inequalities generalizing Ancona's work groups. provides possibly new metrizable topology such also prove that has measure 0 with respect harmonic unless hyperbolic.